Some papers closely related to the current one are [1]}, [2]}, [3]}, [4]}.
On the other hand, the coefficient inverse problem for parabolic equations is also very interesting and studied intensively.
We draw the reader's attention to [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]} for important numerical methods and good numerical results.
Besides, the problem of recovering the initial conditions for the hyperbolic equation is very interesting since it arises in many real-world applications.
For instance, the problems thermo- and photo-acoustic tomography play the key roles in biomedical imaging.
We refer the reader to some important works in this field [12]}, [13]}, [14]}.
Applying the Fourier transform, one can reduce the problem of reconstructing the initial conditions for hyperbolic equations to some inverse source problems for the Helmholtz equation, see [15]}, [16]}, [17]}, [18]}, [19]} for some recent results.
